Average Error: 56.7 → 46.4
Time: 10.2s
Precision: 64
Internal Precision: 128
\[\frac{a1 \cdot a2}{b1 \cdot b2}\]
↓
\[0\]

Error

Bits error versus a1

Bits error versus a2

Bits error versus b1

Bits error versus b2

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original56.7
Target58.3
Herbie46.4
\[\frac{a1}{b1} \cdot \frac{a2}{b2}\]

Derivation

  1. Initial program 56.7

    \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
  2. Using strategy rm

  3. Applied add-log-exp54.9

    \[\leadsto \color{blue}{\log \left(e^{\frac{a1 \cdot a2}{b1 \cdot b2}}\right)}\]

  4. Taylor expanded around 0 46.4

    \[\leadsto \color{blue}{0}\]

  5. Final simplification46.4

    \[\leadsto 0\]

Runtime

Time bar (total: 10.2s)Debug logProfile

herbie shell --seed 2018255 +o rules:numerics
(FPCore (a1 a2 b1 b2)
  :name "Quotient of products"

  :herbie-target
  (* (/ a1 b1) (/ a2 b2))

  (/ (* a1 a2) (* b1 b2)))